We consider the distributed complexity of the (degree+1)-list coloring problem, in which each node u of degree d(u) is assigned a palette of d(u)+1 colors, and the goal is to find a proper coloring using these color palettes. The (degree+1)-list coloring problem is a natural generalization of the classical (Δ+1)-coloring and (Δ+1)-list coloring problems, both being benchmark problems extensively studied in distributed and parallel computing. In this paper we settle the complexity of the (degree+1)-list coloring problem in the Congested Clique model by showing that it can be solved deterministically in a constant number of rounds.
@InProceedings{coy_et_al:LIPIcs.ICALP.2023.46, author = {Coy, Sam and Czumaj, Artur and Davies, Peter and Mishra, Gopinath}, title = {{Optimal (Degree+1)-Coloring in Congested Clique}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {46:1--46:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.46}, URN = {urn:nbn:de:0030-drops-180987}, doi = {10.4230/LIPIcs.ICALP.2023.46}, annote = {Keywords: Distributed computing, graph coloring, parallel computing} }
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